Do those abilities require a unit to suffer damage BEFORE combat to trigger or they can be triggered if unit suffered damage during the same combat roll? Why?

They activate during the "commit dice" step of combat. At that point, the unit has not suffered any damage yet, so you can't commit the dice to use those abilities.

When committing dice, if the effect you are committing for causes damage (Bloodthirst), retreat (Superior Tactics), or gaining lore (Catalyst), those abilities resolve during the Suffer Damage, Resolve Retreats, and Gain Lore steps, respectively. All other effects from committed dice seem to happen immediately after the Commit Dice step (though I don't see anything in the rules to back this up.

An example would be the Stunning Blow ability from Rune Golems. If you roll a heroic result, the effect of Stunning Blow is to assign a Stun token. That effect is not causing damage, causing a retreat, or gaining lore, so it happens during the Commit Dice step. Then, subsequent retreats will become damage because the target can no longer resolve retreat effects.

The Viper Legion's Viper's Bite ability is the same. The reason you can commit lore results to cause damage in the same roll in which you poison the target unit is because you can choose the order in which you commit dice. So you can first commit a heroic result to poison the unit, and then you can commit the lore result to deal damage. After that, you move on to resolving damage.

In the case of Bloodthirst, let's say the target has suffered a damage. So you roll the dice and then move on to the Commit Dice step. You commit your heroic result to use Bloodthirst. So we first check: has the target suffered damage? Yes. So we will cause 1 damage. Additional effects that cause damage are not resolved in the Commit Dice step, but are held until the suffer damage step. During that step, the target would suffer an additional damage on top of any strike or cleave results we rolled. But if the target had NOT suffered damage, we would attempt to commit the heroic result and we would check: has the target suffered damage? No. So we cannot cause 1 damage. So when we get to the suffer damage step, there is no extra damage for the target to suffer.